Vinod can grade a whole set of examination scripts in 30 days at a steady pace. He holds that pace for the first 12 days, after which his daily output falls to two-thirds of what it was. How many days does the whole set take him?

At the full pace he does 1/30 of the set a day, so 12 days cover 12/30 = 2/5. His reduced pace is (2/3)(1/30) = 1/45 of the set a day, and the remaining 3/5 therefore needs (3/5) ÷ (1/45) = 27 days. Total 12 + 27 = 39 days. 30 days ignores the slowdown. 45 days applies the reduced pace to the whole set, forgetting the 12 fast days already banked. 66 days reads "falls to two-thirds" as "falls by two-thirds", leaving a rate of 1/90 and 54 days for the remainder.